Abstarct: Aabstract The Expected Shortfall (ES) is one of the most important regulatory risk measures in finance, insurance, and statistics, which has recently been characterized via sets of axioms from perspectives of portfolio risk management and statistics. Meanwhile, there is large literature on insurance design with ES as an objective or a constraint. A visible gap is to justify the special role of ES in insurance and actuarial science. To fill this gap, we study characterization of risk measures induced by efficient insurance contracts, i.e., those that are Pareto optimal for the insured and the insurer. One of our major results is that we characterize a mixture of the mean and ES as the risk measure of the insured and the insurer, when contracts with deductibles are efficient. Characterization results of other risk measures, including the mean and distortion risk measures, are also presented by lixnking them to different sets of contracts, To validate the research, the obtained insurance data in the field of Insurance-Supplemental treatment activity from Day-Insurance Company are used. baxsed on the risk measures such as, ES, E and VaR the insurance loss of the company and insurance groups is measured and Pareto optimal contracts and Pareto frontier are determined. The results show that Group 28’s insurance contract is Pareto-optimal under all risk measures. Therefore, this contract can be presented as a pattern contract.